학술논문

Archetypal analysis for ordinal data.
Document Type
Journal
Author
Fernández, Daniel (E-UPB-OR) AMS Author Profile; Epifanio, Irene (E-JAU) AMS Author Profile; McMillan, Louise Fastier (NZ-VCTR-SMS) AMS Author Profile
Source
Information Sciences. An International Journal (Inform. Sci.) (20210101), 579, 281-292. ISSN: 0020-0255 (print).eISSN: 1872-6291.
Subject
62 Statistics -- 62H Multivariate analysis
  62H17 Contingency tables
Language
English
Abstract
Summary: ``Archetypoid analysis (ADA) is an exploratory approach that explains a set of continuous observations as mixtures of pure (extreme) patterns. Those patterns (archetypoids) are actual observations of the sample which makes the results of this technique easily interpretable, even for non-experts. Note that the observations are approximated as a convex combination of the archetypoids. Archetypoid analysis, in its current form, cannot be applied directly to ordinal data. We propose and describe a two-step method for applying ADA to ordinal responses based on the ordered stereotype model. One of the main advantages of this model is that it allows us to convert the ordinal data to numerical values, using a new data-driven spacing that better reflects the ordinal patterns of the data, and this numerical conversion then enables us to apply ADA straightforwardly. The results of the novel method are presented for two behavioural science applications. Finally, the proposed method is also compared with other unsupervised statistical learning methods.''